H2O2 oxidizes pathogens.It's as good for sterility.
It's also MUCH better to put a swab with H2O2 on the injection site after the injection because not only it provides sterility but also reduces bleeding (haemostatic) whereas alcohol promotes it.
I use alcohol before and H2O2 after.

Surgeons also use povidone iodine (betadine) on the operation site for almost complete sterile conditions.